Water – How to treat and store an unused water heater to protect it

First thing to check is the faucet aerator. You're probably right about kicking sediment up and clogging something, if you're lucky its just the aerator. It'd take a big piece or a lot of sediment to completely clog a 1/2"-3/4" pipe.

If it's not the aerator, and it's just a single faucet, you have to work backwards starting with the supply lines connecting the faucet to the shut-off valve, all the way back to the water heater.

It's mostly the gas pipe. A tankless water heater is going to need a 1" or even 1.5" pipe to feed it. Your current water heater probably uses a 1/2" pipe. The new pipe probably needs to come off the main trunk, and replacing it requires a precise gas volume calculation and gas plumbing work that is very skilled labor and not cheap. If your plumber can't do this work himself, he's probably subbing it out and you're eating the cost.

Secondarily, there's also the re-plumbing of the water lines to feed the new heater. The inlet and outlet ports are probably in different places compared to where they are on your tank water heater. By contrast, if you replace it with another tank water heater, the water lines are already in the right place, and all you need to do is connect the tank with flex lines.

Finally, the exhaust may be different, too. Particularly if you go with a high-efficiency model, it can't be exhausted through the current pipe that's likely going through the roof.